There are some gold and white balls in a box. If 10 gold balls are removed from the box, the total number of balls left will be 8 times the number of gold balls left. If 40 white balls are removed from the box, the total number of balls left will be 3 times the number of gold balls. How many balls are there in the box?

	Case 1		Case 2
	Gold balls	White balls	Gold balls	White balls
Before	1 u + 10	7 u	1 p	2 p + 40
Change	- 10			- 40
After	1 u	7 u	1 p	2 p

Number of white balls in the end for Case 1
= 8 u - 1 u
= 7 u

Number of gold balls in the end for Case 2
= 3 p - 1 p
= 2 p

The number of gold balls at first is the same for Case 1 and Case 2.
The number of white balls at first is also the same for Case 1 and Case 2.

1 u + 10 = 1 p --- (1)

7 u = 2 p + 40
7 u - 40 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 20 = 2 p --- (3)

(2) = (3)
7 u - 40 = 2 u + 20
7 u - 2 u = 20 + 40
5 u = 60

1 u = 60 ÷ 5 = 12

Number of balls in the box
= (1 u + 10) + 7 u
= 8 u + 10
= (8 x 12) + 10
= 96 + 10
= 106

Answer(s): 106